search
Search
Unlock 100+ guides
search toc
close
account_circle
Profile
exit_to_app
Sign out
What does this mean?
Why is this true?
Give me some examples!
search
keyboard_voice
close
Searching Tips
Search for a recipe:
"Creating a table in MySQL"
Search for an API documentation: "@append"
Search for code: "!dataframe"
Apply a tag filter: "#python"
Useful Shortcuts
/ to open search panel
Esc to close search panel
to navigate between search results
d to clear all current filters
Enter to expand content preview
Doc Search
Code Search Beta
SORRY NOTHING FOUND!
mic
Start speaking...
Voice search is only supported in Safari and Chrome.
Shrink
Navigate to

NumPy | dot Method

schedule Aug 11, 2023
Last updated
local_offer
PythonNumPy
Tags
mode_heat
Master the mathematics behind data science with 100+ top-tier guides
Start your free 7-days trial now!

NumPy's dot(~) is an extremely useful method that can be used to compute the product between:

• scalar and scalar

• vector and vector (dot product)

• matrix and vector

• matrix and matrix

Parameters

1. a | number or array_like

The first argument.

2. b | number or array_like

The second argument.

Return value

The following table summaries what operation is performed as well as the return type:

a

b

operation

Return type

scalar

scalar

Scalar multiplication

number

1D array

1D array

Vector dot product

number

2D array

1D array

Matrix-vector product

1D Numpy array

2D array

2D array

Matrix-matrix multiplication

2D Numpy array

n-D array

n-D array

Batch products

n-D Numpy array

Examples

Dotting two numbers (scalar and scalar)

 np.dot(2, 3) 6 
WARNING

Avoid this for scalar multiplication. If you just want to multiply two scalar numbers, just use the standard 2 * 3 - it's faster and clearer.

Dotting two arrays (vector and vector)

 # (1 * 3) + (2 * 4) = 11np.dot([1,2], [3,4]) 11 

Mathematically, we're doing the following:

$$\begin{pmatrix} 1\\ 3\\ \end{pmatrix} \cdot \begin{pmatrix} 2\\ 4\\ \end{pmatrix}= 11$$

Just as a side note, the parameters just have to be array-like; we can use NumPy arrays as well:

 x = np.array([1,2])y = np.array([3,4])np.dot(x, y) 11 

Matrix-vector multiplication

 X = np.array([[1,2],[3,4]])y = np.array([5,6])np.dot(X,y) array([17, 39]) 

Mathematically, we're doing the following:

$$\begin{pmatrix} 1&2\\ 3&4\\ \end{pmatrix} \begin{pmatrix} 5\\ 6\\ \end{pmatrix}= \begin{pmatrix} 17\\ 39\\ \end{pmatrix}$$

Matrix-matrix multiplication

 x = [[1,0], [0,1]]y = [[2,2], [2,2]]np.dot(x, y) array([[2, 2],       [2, 2]]) 

Mathematically, we're doing the following:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 2&2\\ 2&2\\ \end{pmatrix}= \begin{pmatrix} 2&2\\ 2&2\\ \end{pmatrix}$$

Always remember that parameters just have to be array-like; we can use NumPy arrays as well:

 x = np.array([[1,0], [0,1]])y = np.array([[2,2], [2,2]])np.dot(x, y) array([[2, 2],       [2, 2]]) 
WARNING

Avoid this for matrix multiplication. If you want to take the product of two matrices, use NumPy's matmul(~) method or the @ notation instead.

Batch products

The dot(~) method can be used to compute multiple products at once, like follows:

 x = [ [[1,0], [0,1]], [[1,1], [1,1]] ]y = [3,4]np.dot(x,y) array([[3, 4],       [7, 7]]) 

In this example, the variable $x$ holds the following two matrices:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \;\;\;\; \begin{pmatrix} 1&1\\ 1&1\\ \end{pmatrix}$$

The final line, np.dot(x,y), is performing the following mathematical operations:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 3\\ 4\\ \end{pmatrix}= \begin{pmatrix} 3\\ 4\\ \end{pmatrix}$$
$$\begin{pmatrix} 1&1\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 3\\ 4\\ \end{pmatrix}= \begin{pmatrix} 7\\ 7\\ \end{pmatrix}$$

Note that batch products also for vector-vector product and matrix-matrix product as well.

Edited by 0 others
thumb_up
thumb_down
Comment
Citation
Ask a question or leave a feedback...
thumb_up
0
thumb_down
0
chat_bubble_outline
0
settings
Enjoy our search
Hit / to insta-search docs and recipes!